Now, I know mathematicians don't like reading but if you want to take a degree in Maths, it might be nice to have a book to talk about in your interview. And the physicists have got a list, so we ought to have one too. Here's the collated recommendations from various threads on the site. I give multiple recommendations for the same book to give a feel for popularity.
- Does God Play Dice by Ian Stewart
- Chaos by James Gleick
Quite Physicsy, but a good read, yet again quite biographical, some have said that it gets hard work to read quite soon after opening! MrMathsGenius. NB: I've seen this dissed a couple of times on the threads that provide the source for this page. Mr Dactyl
- The Codebook by Simon Singh
Recommended here. Interesting exploration into the different types of codes and CYPHERS used throughout history. Is a very good GENERAL MATHS BOOK, covering elements of basic number theory, physics (potential of photon money!), statistics (frequency Analysis) and computing. I found it interesting but view it more as an encyclopedia for reference rather than a comprehensive account. Says MrMathsGenius.
- The Mathematics of Ciphers by S.C. Coutinho
- In Code by Sara Flannery
History of Mathematics
- A History of Mathematics by Carl B. Boyer
- Infinity: The Quest to Think the Unthinkable by Brian Clegg
Am currently reading this. This is definitely one of the better books on the subject. A chronological biography of the concept of infinity, from Greeks to present day. Says MrMathsGenius.
- E, the Story of a Number by Eli Maor
- The Man Who Loved Only Numbers by Paul Hoffman
An excellent account of one of the 20th Century's most prolific mathematicians.
- My Brain is Open: The Mathematical Journeys of Paul Erdos by Bruce Schecter
Yet another biographical book, but well worth the read! Not that much maths in it, but looks interesting. MrMathsGenius.
- The Man who knew Infinity by Robert Kanigel
Book about Ramanujan, yet again more biographical, but still worth a look.
- A Brief History of Time by Stephen Hawking
- The Elegant Universe by Brian Greene
A book about string theory, but most of the book is about relativity and quantum mechanics etc, says Speleo.
- The Fabric of the Cosmos by Brian Greene
Sequel to the above. Focuses more on new research. Both books are very interesting.
- Introduction to Mathematical Philosophy by Bertrand Russell
- A Mathematician's Apology by G. H. Hardy
Recommended here and here. Beginning to look decidedly old-fashioned, and Hardy makes some points which are clearly wrong about the role of mathematics in society. When he talks about the subject itself, he is powerful. This is a classic, and widely read. Try to find the version with introduction by CP Snow.
- Thinking About Mathematics by Stewart Shapiro
A good introduction to the philosophy of maths, presents an overview of the history and current positions in the field. Likely to be of less interest to those interested in straight maths, though.
- Fermat's Last Theorem by Simon Singh
Recommended here, here, here, here, here, here, here, here, here, here, here and here. So basically, everyone reads this. You won't stand out at all. An enjoyable read all the same and "you must read this story" according to Cambridge's Faculty of Maths.
- The Millenium Problems by Keith Devlin
- Journey Through Genius: The Great Theorems of Mathematics by William Dunham
Strongly recommended here.
- The Equation That Couldn't Be Solved by Mario Livio
- Kepler's Conjecture by George Szpiro
- Poincaré's Prize by George Szpiro
- The Music of the Primes by Marcus du Sautoy
- Four Colors Suffice by Robin Wilson
- Godel, Escher, Bach by Douglas Hofstadter
A book about formal logic, Godel's Incompleteness theorems, and about 400 tedious pages on neuroscience and music. It's very interesting in parts, the dialogues especially are wonderful, but about half the book has nothing to do with maths and is tedious beyond belief, says Speleo. And here and here.
- Concepts in Modern Mathematics by Ian Stewart
- Geometry for Dummies by Mark Ryan
- Concise Introduction to Pure Mathematics by Martin Liebeck
Definitely not very heavy, but nonetheless, an interesting/relaxing read about imaginary numbers and a vast array of other topics:
- Mathematical Methods for Science Students by G Stephenson
A very clear and readable text useful for introducing some university level concepts to the top end of the A level cohort. The book starts off easy and gradually progresses onto some very interesting mathematics such as multivariable calculus and a study of the gamma function.
- The Emperor's New Mind by Roger Penrose
- The Mathematical Universe by William Dunham
- The Wonders of Numbers by Clifford Pickover
- From Here to Infinity by Ian Stewart
- The Art of the Infinite: Our Lost Language of Numbers by Robert Kaplan
- What is Mathematics? by Richard Courant, Herbert Robbins and Ian Stewart
- Flatterland by Ian Stewart
Fantastic take on a 19th century book about different geometries, starts by explaining 4d by exploring the way our 3d world would look to a 2d or 1d person! Recommended here.
- The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger
Recommended here. An entertaining book, and certainly one for younger people looking for some interesting, yet accessible, mathematics.
- Art of the Infinite by Kaplan
- Imagining Numbers: Particularly the Square Root of Minus Fifteen by Barry Mazur
Good(ish). Mazur takes the scenic route to complex numbers, via a deep exploration of their history and a brief tour of the science of the imagination. No challenging maths, but a readable book. Recommended here.
- A Very Short Introduction to Mathematics by Timothy Gowers
Tiny, incredibly dense book written by a Fields Medallist. Provides a great jumping off point for further independent reading around maths, and a glimpse of the character of 'real maths'. User:Mr Dactyl
Linear Algebra Step by Step by Singh. It has complete solutions to all the problems in the book and also has fresh problems on the book's website at http://global.oup.com/booksites/content/9780199654444/
These books are not about mathematics but rather contain mathematics for you to do.They are not standard undergraduate books but rather contain topics not covered in a typical undergraduate and often graduate program.Very different from all other math books here.But beware,not all of them are easy!
- ""Abel's Theorem in Problems and Solutions: Based on the Lectures of Professor V.I. Arnold"" by V. B. Alekseev
Vladimir Arnol'd was one one of the greatest mathematicians of the previous century but more importantly he is one of the greatest mathematics teachers ever! This is evident in his writings three of which have been included here.However a simple search will reveal a lot more.In this book he proves that a general fifth degree equation does not have a formula for its roots(i.e. is not solvable by radicals).He does so by considering the monodromy group of the riemann surface of all possible candidate multi-valued function to obtain a contradiction! This is a mouthful isn't it.But the most remarkable thing is that this book is based on lectures given to 16 year olds.Read this book and solve the problems to learn about groups,fundamental group,riemann surface and a lot more.
- ""Lectures and Problems: A Gift to Young Mathematicians "" by V.I. Arnold
A great book with a collection of accessible topics and interesting but difficult problems.
- ""Mathematical Understanding of nature"" by V.I. Arnold
Another masterpiece by Arnold.This book explains how advanced mathematics explains complicated natural phenomenon.For example when you stir a cup of tea what is the shape that the surface assumes.
- ""Mathematical Omnibus: Thirty Lectures on Classic Mathematics "" by Tabachnikov and Fuchs
This is a remarkable book that gives you a glimpse into vast and beautiful world of contemporary mathematics research.Some of the 30 lectures require you to know basic calculus others don't.This is a great book if you are keen to see what "real" mathematics looks like.
- ""Mathematical Puzzles: A Connoisseur's Collection"" by Peter Winkler
This book is a collection of annoyingly elusive and difficult problems in mathematics.It does not require you to know any advanced mathematics but the problems are HARD! These problems require you to think outside the box there is no technique or skill involved just thinking.When you do solve one of them it feels GREAT!
- ""MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics"" by Svetlana Katok, Alexei Sossinsky, Serge Tabachniko
This book is possibly the hardest book on the list.Maybe it does not belong here.Just for the masochists among you who think they can tackle a book that would be difficult for the best of the best undergraduate students in the top universities can try this one.
- ""Glimpses of Algebra and Geometry"" by Gabor Toth
This book has a lot of advanced content.But this book is perhaps much easier than most of the books in this sections.The problems are easier the proofs are more accessible.Only problem is that it sometimes requires a lot more prerequisites than the other books here.Even if you dont know anything more that differential calculus you can still read more than two-thirds of this book and enjoy it as well.The other third unfortunately requires you to know some undergraduate concepts.
- ""Numbers and Geometry"" by John Stillwell
This is the best book to prepare for an undergraduate maths degree.Everything you have seen in GCSE will reappear in this book in completely different form.I cannot express how helpful reading this book will be if you want to do well in a maths degree.It will teach you how to think like a mathematician.This is also the easiest book in this section.While you are at it check out some other stuff by Stillwell as well specially Geometry of surfaces and Classical Topology and Combinatorial Group Theory.
Other Reading Lists
- Oxford is here.
- Cambridge is here.
- Balliol '04 here.